The paper presents an analysis of factors influencing the accuracy of reproduction of geometry of the vertebrae and the intervertebral disc of the lumbar motion segment for the purpose of designing of an intervertebral disc endoprosthesis. In order to increase the functionality of the new type of endoprostheses by a better adjustment of their structure to the patient’s anatomical features, specialist software was used allowing the processing of the projections of the diagnosed structures. Recommended minimum values of projection features were determined in order to ensure an effective processing of the scanned structures as well as other factors affecting the quality of the reproduction of 3D model geometries. Also, there were generated 3D models of the L4-L5 section. For the final development of geometric models for disc and vertebrae L4 and L5 there has been used smoothing procedure by cubic free curves with the NURBS technique. This allows accurate reproduction of the geometry for the purposes of identification of a spatial shape of the surface of the vertebrae and the vertebral disc and use of the model for designing of a new endoprosthesis, as well as conducting strength tests with the use of finite elements method.